Logarithmic distribution
: This can be found in
extraDistr,
VGAM,
actuar
and
gamlss.dist.
Zero-modified and zero-truncated versions is provided in
actuar.
A fast random generator is
available for the logarithmic distribution
is implemented in
Runuran
as well as the 'density' function.

Poisson distribution
: provided in
stats
and in
poweRlaw.
Zero-modified, zero-inflated, truncated versions are provided
in
extraDistr,
gamlss.dist,
actuar
and in
VGAM.
extraDistr
provides the truncated Poisson distribution.
LaplacesDemon
provides the generalized Poisson distribution.
See the mixture section such as the Poisson-lognormal mixture.

Negative binomial distribution
: provided in
stats
.
Zero-modified, zero-inflated, truncated versions are provided
in
gamlss.dist,
extraDistr,
actuar
and in
VGAM.
New parametrization of the negative binomial distribution
is available in
RMKdiscrete.

Zipf law
:
d, p, q, r functions of the Zipf and the Zipf-Mandelbrot distributions
are provided in
tolerance,
VGAM.
Package
zipfR
provides tools for distribution of word frequency,
such as the Zipf distribution.

Beta distribution and its extensions
:
Base R provides
the d, p, q, r functions for this distribution (see above).
extraDistr
provides the beta distribution
parametrized by the mean and the precision.
actuar
provides moments and limited expected values.
sadists
implements Gram Charlier, Edgeworth and Cornish-Fisher approximations
for doubly non central beta distribution for computing d, p, q, r functions.
extraDistr
provides the four-parameter beta with lower and upper bounds.
The generalized beta of the first kind (GB1) (exponentation of beta 1)
is provided in
gamlss.dist,
mbbefd,
actuar.
The beta prime (or beta of the second kind), which is the distribution of X/(1-X) when
X follows a beta distribution of the first kind,
is provided in
VGAM,
extraDistr,
LaplacesDemon
and
mc2d.
The zero and one inflated beta distribution can be found in
gamlss.dist.
The generalized beta of the second kind (GB2) is provided in
gamlss.dist,
GB2.
Several special cases of the generalized beta distribution are
also implemented in
VGAM,
mc2d: Lomax, inverse Lomax, Dagum, Singh-Maddala, Pert distributions.
actuar
provides the transformed beta 2 distribution which includes
as special cases Burr, loglogistic, paralogistic, generalized Pareto, Pareto,
see also the Pareto subsection.

Bridge distribution
: provided in
bridgedist,
as detailed in Wang and Louis (2003).
The distribution of random intercept that allows a marginalized
random intercept logistic regression to also be logistic
regression.

Chi(-squared or not) distribution
: Base R provides
the d, p, q, r functions for the chi-squared distribution, both central
and non-central (see above).
Moments, limited
expected values and the moment generating function are provided in
actuar.
extraDistr
provides d, p, q, r functions for inverse chi-squared
distribution (standard and scaled).
Only d,r functions are available for the inverse chi-squared distribution
in package
geoR
and
LaplacesDemon.
A fast random generator is available for the Chi distribution
is implemented in
Runuran
as well as the density function.
The non-central Chi distribution is not yet implemented. The chi-bar-squared distribution
is implemented in
emdbook.
sadists
implements Gram Charlier, Edgeworth and Cornish-Fisher approximations
for sums of non central chi-squared raised to powers distribution and sums of log of
non central chi-squared for computing d, p, q, r functions.

Exponential distribution and its extensions
: Base R provides the d, p, q, r functions
for this distribution (see above).
actuar
provides additional functions
such as the moment generating function, moments and limited expected values. It also has
the d, p, q, r for the inverse exponential distribution.
The shifted (or two-parameter exponential) and the
truncated exponential distributions are implemented in
lmomco
and
tolerance
packages with d, p, q, r functions.
Exponential Power distribution is also known as General Error Distribution:
d, p, q, r functions for the power and the skew power exponential
type 1-4 distributions are implemented
in
gamlss.dist
and
lmomco.
The power exponential distribution is also provided in
normalp,
LaplacesDemon
and
sgt.
The skew power exponential is provided
sgt.
reliaR
provides
the generalized exponential, the inverse generalized exponential,
the logistic exponential, the Marshall-Olkin Extended Exponential and
the exponential extension distributions.
A fast random generator is available for the power Exponential distribution
is implemented in
Runuran
as well as the density function.
rpgm
provides a fast random number generator for the exponential distribution.

Frechet distribution
: provided in
VGAM,
RTDE,
ReIns,
extraDistr
and
evd. A fast random generator is
available for the Frechet distribution
is implemented in
Runuran
as well as the density function.
The truncated Frechet distribution is provided in
ReIns.

(Tukey) Lambda distribution and its extensions
:
The generalized Lambda distribution (GLD) is well known for its wide range of shapes.
The original Tukey Lambda distribution can be obtained as a special
case of the generalized Lambda distribution.
There exists different parametrization of GLD in the literature:
RS (Ramberg-Schmeiser or tail-index param),
FMKL (Freimer-Mudholkar-Kollia-Lin),
FM5 (Five-parameter version of FKML by Gilchrist),
GPD (gen. Pareto dist.)
and AS (Asymmetry-steepness). The following packages implement such distributions
(with d, p, q, r functions):
gld
(RS, FKML, FM5, GPD),
Davies
(RS),
gb
(RS),
lmomco
(FMKL),
extraDistr
(original Tukey).
ecd
provides the elliptic lambda distribution and its use for
financial pricing.

Laplace (also called double exponential distribution)
and asymetric Laplace distribution
:
provided in
distr,
lmomco,
LaplacesDemon,
VGAM,
sgt,
extraDistr
and
HyperbolicDist
packages.
LaplacesDemon
provides the Laplace distribution parametrized
by the precision parameter as well as the skew Laplace distribution.
Asymetric Laplace distribution is implemented in
ald.
A fast random generator is available for the Laplace distribution
is implemented in
Runuran
as well as the density function.
smoothmest
implements the density and the random generator.
The skew Laplace distribution is available in
sgt.
LaplacesDemon
provides the log-Laplace distribution.

Logistic distribution and its extensions
: Base R provides
the d, p, q, r functions for this distribution (see above).
actuar
and
VGAM
provide d, p, q, r functions for
the log logistic (also called Fisk), the paralogistic and the inverse paralogistic distributions.
FAdist
the log-logistic distribution with two and three parameters.
The generalized logistic distribution (Type I, also known as skew-logistic distribution) is provided
in
lmomco,
sld,
SCI
and
glogis. Finally,

Log-normal distribution and its extensions
:
The log normal distribution is implemented in Base R (see above)
and
poweRlaw.
The log normal distribution parametrized by its mean and
its coefficient of variation is also provided in
EnvStats.
LaplacesDemon
provides the lognormal parametrized by
the precision parameter.
The truncated lognormal distribution is provided in
EnvStats
with two possible parametrizations as well as in
ReIns.
The 3-parameter lognormal
distribution is available in
lmomco,
EnvStats
and
FAdist.
The package
loglognorm
implements d, p, q, r functions for the double lognormal distribution,
as well as the raw moment, the expected value and the variance functions.
EnvStats
provides d, p, q, r functions for the zero-modified lognormal
distribution with two possible parametrizations.
rpgm
provides a fast random number generator for the lognormal distribution.

Pearson's distribution
: Pearson type III available
in
lmomco
and
FAdist.
A log-Pearson type III distribution is also available in
FAdist.
PearsonDS
provides the d, p, q, r functions as well as the first
four moments for the Pearson distributions: types I, II, III, IV, V, VI, VII.

Triangle/trapezoidal distribution
: packages
triangle,
extraDistr,
mc2d,
EnvStats
and
VGAM
provide d, p, q, r functions for the triangle or triangular distribution, while the package
trapezoid
provides d, p, q, r functions for the Generalized Trapezoidal Distribution.
A fast random generator is available for the triangle distribution
is implemented in
Runuran
as well as the density function.

Tsallis or q-Exponential distribution
:
tsallisqexp
provides d, p, q, r functions for two parametrizations of
the Tsallis distribution and also implements a left-censored version.

Tweedie distribution
: the Tweedie distribution is implemented
in package
tweedie. Let us note that the Tweedie distribution
is not necessarily continuous, a special case of it is the Poisson distribution.

Weibull distribution and its extensions
: Base R provides
the d, p, q, r functions for this distribution (see above).
The inverse Weibull is provided in
actuar
package and also the moments
and the limited expected value for both the raw and the inverse Weibull distribution.
FAdist
implements the three-parameter Weibull distribution, while
reliaR
implements the exponential Weibull, the flexible Weibull,
the generalized power weibull, the Marshall-Olkin Extended Weibull and
the Weibull extension distributions.
Furthermore,
lmomco
implements the Weibull distribution while
evd
implements the reverse Weibull distribution.
The reverse generalized extreme value distribution are provided in
gamlss.dist
(d, p, q, r) and the shifted left truncated Weibull distribution
is provided in
Renext.
The right truncated Weibull is provided in
ReIns.

Multivariate Cauchy distribution
:
sn
provide d, p, r functions for the multivariate skew Cauchy distribution,
while
LaplacesDemon
provides d, r functions for the multivariate
Cauchy distribution parametrized either by sigma,
by the Cholesky decomposition of sigma, by the precision matrix
omega or by the Cholesky decomposition of omega.

Multivariate exponential distribution
:
while
LaplacesDemon
provides d, r functions for the multivariate
power exponential distribution parametrized either by sigma,
or by the Cholesky decomposition of sigma.

One-inflated distributions
:
a generic distribution as well as special cases (OI-beta, OI-uniform, OI-GB1, OI-Pareto)
are provided in
mbbefd.
The zero and one inflated beta distribution can be found in
gamlss.dist.

Discretized distribution
:
distcrete
allows discretised versions of continuous distribution by mapping
continuous values to an underlying discrete grid, based on a (uniform) frequency of
discretisation, a valid discretisation point, and an integration range.

Order statistics
:
Distribution function of the jth order statistic can be obtained with base R functions.
ORDER2PARENT
transforms distribution function of order statistics to its parent
distribution function.

Wishart distributions
:
Base R provides the r function for the Wishart distribution.
the d, r functions are provided in
MCMCpack,
RMTstat
and
bayesm.
LaplacesDemon
provides Wishart distribution
parametrized either by Sigma or by its Cholesky
decomposition.

Unified approaches
:
The packages
fCopulae,
copula, and
copBasic
provide a lot of
general functionality for copulas. Although lacking support for
many existing copulas themselves,
copBasic
is primarily oriented
around utility functions for the general mathematics of copulas
as described in the well known introduction to copulas by Nelsen.

Basic functionality
: R provides several random number generators (RNGs).
The random seed can be provided via
set.seed
and the kind of RNG can be specified
using
RNGkind. The default RNG is the Mersenne-Twister algorithm.
Other generators include Wichmann-Hill, Marsaglia-Multicarry, Super-Duper,
Knuth-TAOCP, Knuth-TAOCP-2002, as well as user-supplied RNGs. For normal
random numbers, the following algorithms are available: Kinderman-Ramage,
Ahrens-Dieter, Box-Muller, Inversion (default). In addition to the tools above,
setRNG
provides an easy way to set, retain information about the setting, and reset the RNG.

Pseudo-randomness
:
RDieHarder
offers several dozen new RNGs
from the GNU GSL.
randtoolbox
provides
more recent RNGs such as SF Mersenne-Twister and WELL,
which are generators of Mersenne Twister type, but with
improved quality parameters.
rngwell19937
provides one of the WELL generators with 53 bit
resolution of the output and allows seeding by a vector
of integers of arbitrary length.
randaes
provides the deterministic part of the Fortuna cryptographic
pseudorandom number generator (AES).
SuppDists
implements two RNGs of G. Marsaglia.

Support for several independent streams:
rstream
focuses on multiple independent streams of random numbers
from different sources (in an object oriented approach).

For non-uniform generation, the
Runuran
package interfaces to the UNU.RAN library for universal non-uniform generation
as well as customised distributions based on polynomial interpolation of the inverse
cumulative distribution function.
rust
performs non-uniform random variate generation from unimodal
(low-dimensional) multivariate continuous distributions, using the
generalized ratio-of-uniforms method.

Benchmark
: A set of 28 densities suitable for comparing
nonparametric density estimators in simulation studies can be found
in the
benchden
package. The densities vary greatly in degree of
smoothness, number of modes and other properties. The package
provides d,p,q and r functions.

Non parametric models
:

Binned Empirical distributions
: The
HistogramTools
package
provides a number of methods for manipulating empirical data that has
been binned into histogram form, including: (1) the empirical
cumulative distribution function, (2) the empirical quantile, and (3)
information loss metrics associated with binning.

Transformation
: Lebesgue decomposition are implemented
in
distr, as well as Convolution, Truncation and Huberization of distributions.
Furthermore,
distr
provides distribution of the maximum or minimum
of two distributions. See Object-orientation above.

User Interface
:
AtelieR
package provides a GTK GUI for teaching basic
concepts in statistical inference, implementing all the R base distributions
as well as the generalized Student, the inverse Chi-square, the inverse gamma
and the lambda-prime distributions.